A standard isotherm of copper

Abstract

Constructing wide-ranging equations of state for various materials is a challenging problem. Its essential part is finding zero isotherms, i.e., global curves of cold compression P(ρ) applicable at pressures 0 ≤ P < ∞ (ρ is the density of a material). Models of a planet’s structure, regimes of shock-free compression of thermonuclear targets, etc., are very sensitive to these isotherms. The initial segments of these curves are obtained from experiments on static and shock-wave compressions, while the upper segments are derived from theoretical calculations. However, a wide interval for which there are no reliable data remains between these segments. This interval is filled with approximated data based on model considerations. A number of reasonable approximations were constructed in studies performed in our country in 1960– 1990. There were no other similar publications abroad, although such approximations were presumably constructed. This conclusion follows from the existence of the Los Alamos SESAME library for materials properties. We compared these studies and found that the differences between P(ρ) curves in them reach 25%, and none of the curves has a convincing justification. Therefore, the problem of constructing precision curves remained unsolved. Here, we propose a method of constructing P(ρ) curves for materials that undergo no phase transitions. As an example, we chose copper. Its fcc crystal lattice is close packed, and the metal has no phase transitions under static compression. Copper possesses plasticity, which provides for isotropy of static compressions and their good conformity with dynamic ones. Copper melts under dynamic compressions, but this transition is almost imperceptible. For copper, the number of experimental measurements is rather large, and their accuracy is higher than for other materials. Therefore, copper is the most suitable material for a standard. Below, we construct the precision room-temperature isotherm of copper (it is more convenient than the zero isotherm). Under compressions smaller than 2.4-fold and higher than 60-fold, the error of the iso-